/*
 * RationalLine.java
 *
 * Created on December 9, 2005, 5:38 PM
 */

package Current.basic;

import java.awt.geom.*;

/**
 * A rational line is a linear condition on the angles of a triangle such
 * that all the coefficients are integers (and not all are zero).
 * For instance, if a,b,c are integers then they determine a rational line
 * consisting of the set of all triangles with angles x,y,z for which
 * ax+by+cz=0.
 * @author  pat
 */
public class RationalLine {
    public static final RationalLine[] boundary={
        new RationalLine(1,0,0),
        new RationalLine(0,1,0),
        new RationalLine(-1,1,1),
        new RationalLine(1,-1,1)
    };
    
    // array of coefficients of lines as described above.
    public int[] x=new int[3];
    
    /** Creates a new instance of RationalLine */
    public RationalLine(int a, int b, int c) {
        x[0]=a;
        x[1]=b;
        x[2]=c;
    }
     
    public RationalLine(RationalLine L) {
        x[0]=L.x[0];
        x[1]=L.x[1];
        x[2]=L.x[2];
    }
    
    public RationalLine(RationalTriangle a, RationalTriangle b) {
        x=BasicMath.cross(a.x,b.x);
        reduce();
    }    
    
    public double dot(Complex z) {
        return x[0]*z.x+x[1]*z.y+x[2]*(2-z.x-z.y);
    }
    
    public boolean equals(RationalLine L) {
        if (L==null)
            return false;
        return (x[0]==L.x[0])&&(x[1]==L.x[1])&&(x[2]==L.x[2]);
    }
    
    public void reduce() {
        int gcd=BasicMath.gcd(x);
        if (gcd!=0) {
            x[0]/=gcd;
            x[1]/=gcd;
            x[2]/=gcd;
        }
        // normalize so that the last nonzero coordinate is positive.
        boolean change=false;
        for (int i=2; i>=0; i--) {
            if (x[i]<0) {
                change=true;
                break;
            }
            if (x[i]>0) {
                change=false;
                break;
            }
        }
        if (change)
            for (int i=2; i>=0; i--)
                x[i]*=-1;
    }
    
    public boolean isZero() {
        return (x[0]==0)&&(x[1]==0)&&(x[2]==0);
    }
    
    /** returns true if the line intersects the closure of the square */
    public boolean isBoundaryValid() {
        for (int i=0; i<4; i++) {
            RationalTriangle p=new RationalTriangle(this, boundary[i]);
            if (p.isBoundaryValid())
                return true;
        }
        return false;
    }
    
    /** Returns a line that can be drawn in McBilliards coordinates on the
     * parameter space. Returns null, if the intersection with the McBilliards square is
     * empty. */
    public Line2D.Double toLineSegment(){
        RationalTriangle[] ret=new RationalTriangle[2];
        int i=0;
        for (int j=0; j<4; j++) {
            ret[i]=new RationalTriangle(this, boundary[j]);
            //System.out.println("pt: "+i+" : "+ret[i]);
            if (ret[i].isBoundaryValid()){
                i++;
            } else {
                //System.out.println("invalid");
            }
            if (i==2)
                if (!((new RationalLine(ret[0], ret[1])).isZero())) {
                    return new Line2D.Double(ret[0].toPoint(),ret[1].toPoint());
                } else {
                    //System.out.println("failed test");
                    i--;
                }
        }
        return null;
    }
    
    public String toString() {
        return "("+x[0]+", "+x[1]+", "+x[2]+")";
    }
    public String toSaveString(){
        return ""+x[0]+" "+x[1]+" "+x[2];
    }
    public String toStringEquation() {
        return ""+x[0]+"x+"+x[1]+"y+"+x[2]+"z=0";
    }
    public String toStringFunction() {
        return ""+x[0]+"x+"+x[1]+"y+"+x[2]+"z";
    }
    
    public void neg() {
        x[0]*=-1;
        x[1]*=-1;
        x[2]*=-1;
    }
}